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Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String

Secured at both ends, a steel wire possesses a fundamental frequency of 200 Hz . A person is capable of hearing sound up to a maximum frequency of 14 kHz . Determine the highest harmonic that can be produced on this string and still remain audible to the person.

Options

  1. A70
  2. B7
  3. C700
  4. D140

Correct answer

A. 70

Step-by-step solution

The fundamental frequency of the string is given as f₁ = 200 Hz . The maximum audible frequency for the person is f_ max = 14 kHz = 14000 Hz . The frequency of the n^ th harmonic of a string secured at both ends is given by f_ n = n f₁ . For the sound to remain audible, the frequency of the harmonic must be less than or equal to the maximum audible frequency: f_ n f_ max n 200 14000 n 14000 200 n 70 The highest harmonic that can be produced and still remain audible is 70 .

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